Regarding Lambda Functions in C++

I've been working with C++ for a long time, but I've only recently started to play with lambdas. I have the following example which gives me some trouble figuring it out (why does it behave like this). Keep in mind that this is just an example snippet.

double TwoParams::shiftedSquaredSum(double izero, double particlePotential, double shift)
{
    double sum=0;
    bool ok = true;
    int count = 0;
    double temp;

    //the term with index K in the RMS total sum  <------------- MY LAMBDA 
    auto rms = [](double exp, double th) {
        return std::pow(exp - th, 2.0);
    };

    for (int i = 0; i < Lu_163_Exp.dim1 && ok; ++i)
    {
        temp = rms(Lu_163_Exp.spin1Exp[i], band1EnergyShifted(Lu_163_Exp.spin1Exp[i], izero, particlePotential, shift));
        if (isnan(temp))
        {
            ok = 0;
            break;
        }
        if (!isnan(temp))
        {
            count++;
            sum += temp;
        }
    }
return sum;

The terms Lu_163_Exp.spin1Exp[i] are some constant double vectors located in another class which I want to access it from multple .cpp sources, and band1EnergyShifted() is a method declared in the TwoParams class. This method is also of double type.

Now, my issue is this: If the rms lambda has the parameters exp and th of double type, the compilation is succesfull, but if I have it

 auto rms = [](auto exp, auto th) {    // <--------------- I initially wanted to set them with auto type
        return std::pow(exp - th, 2.0);
    };

compilation gives erros:

twoParamsEnergies.cpp: In member function ‘double TwoParams::shiftedSquaredSum(double, double, double)’:
twoParamsEnergies.cpp:62:24: error: parameter declared ‘auto’
     auto rms = [](auto exp, auto th) {
                        ^
twoParamsEnergies.cpp:62:34: error: parameter declared ‘auto’
     auto rms = [](auto exp, auto th) {
                                  ^
twoParamsEnergies.cpp: In lambda function:
twoParamsEnergies.cpp:63:31: error: ‘th’ was not declared in this scope
         return std::pow(exp - th, 2.0);
                               ^
twoParamsEnergies.cpp: In member function ‘double TwoParams::shiftedSquaredSum(double, double, double)’:
twoParamsEnergies.cpp:68:119: error: no match for call to ‘(TwoParams::shiftedSquaredSum(double, double, double)::__lambda0) (double&, double)’
         temp = rms(Lu_163_Exp.spin1Exp[i], band1EnergyShifted(Lu_163_Exp.spin1Exp[i], izero, particlePotential, shift));

From what I've understood so far, the compiler should figure it out by itself the type of exp and th if the parameters are of auto type. Am I missing something?

Thank you in advance!